Sorry, this one is a little long-winded, but I hope it's clear! I've come across a problem that I'm struggling to solve because it *requires* the use of certain standard results as the starting point. The problem is to find the solution of

I can solve this problem quite easily by considering the form of each term in the sum, or through the use of partial fractions (where I find an ultimate answer of , but I'm supposed to solve it using one (or more) of the following standard results (I'll include all of them, but I imagine only the final one is relevant):

n(n + 1)(2n + 1)

n^{2}(n + 1)^{2}

n(n + 1)(n + 2)

I can't figure out how to get from the right-hand side of the standard result to the final answer of . I assume I'm missing something really simple about the relationship between and , but I just can't see it. Any help would be greatly appreciated. Thanks very much.